Projective varieties covered by trivial families

Details Projective varieties covered by trivial families Projective varieties covered by trivial families

2011-10-25

arxiv.org/abs/1110.5661v1

Mathematics

Algebraic Geometry

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Scientific paper

Let k be a field of characteristic zero, C a smooth projective curve defined
over k. Let X,Y be projective schemes over C with Y reduced and g:X \to Y a
morphism defined over C such that $g^{#}: \mathcal{O}_Y \to g_* \mathcal{O}_X$
is an isomorphism. If X \to C is a trivial family, then the generic fiber of
the family Y \to C is isotrivial.

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